3.4 The Derivative as a Rate of Change 1 Chapter 3. Dierentiation 3.4 The Derivative as a Rate of Change Denition. Instantaneous Rate of Change The instantaneous rate of change of f with respect to x at x is the 0 derivati...

3.2 The Derivative as a Function 1 Chapter 3. Dierentiation 3.2 The Derivative as a Function Denition. Derivative Function. The derivative of the function f(x) with respect to the variable x is the function f whose value a...

3.1 Tangents and the Derivative at a Point 1 Chapter 3. Dierentiation 3.1 Tangents and the Derivative at a Point Note. We now return to an idea introduced in Section 2.1: Slopes of lines tangent to curves. Denition. Slope ...

2.3 The Precise Denition of a Limit 1 Chapter 2. Limits and Continuity 2.3 The Precise Denition of a Limit (Read this section of the text! These are the most important 7 pages in this 1200 page book!) Denition. Formal Deni...

2.1 Rates of Change and Tangents to Curves 1 Chapter 2. Limits and Continuity 2.1. Rates of Change and Tangents to Curves Denition. The average rate of change of y = f(x) with respect to x over the interval 1x 2x ] is y f(...

2.2 Limit of a Function and Limit Laws 1 Chapter 2. Limits and Continuity 2.2. Limit of a Function and Limit Laws Note. We have to be careful in our dealings with functions! Notice that x(x 1) f(x) = x 1 and g(x) = x are N...

1.5 Exponential Functions 1 Chapter 1. Functions 1.5. Exponential Functions Note. In Chapter 7 we will use calculus to dene logarithmic and expo nential functions. In this section and the next, we informally deal with thes...

1.3 Trigonometric Functions 1 Chapter 1. Functions 1.3. Trigonometric Functions 0 0 Denition. The number of radians in the central angle A CB within a circle of radius r is dened as the number of radius units contained in ...

1.1 Functions and Their Graphs 1 Chapter 1. Functions 1.1. Functions and Their Graphs Note. We start by assuming that you are familiar with the idea of a set and the set theoretic symbol (an element of). Denition. A functi...

This Guide provides an easy to follow summary of all basic principles that are the foundation to Statistics and Probabilities. Using a combination of charts and sample equations, the key concepts are developed and the esse...

This useful Math Guide is a specific reference for techniques to convert ordinary differential equations to algebraic equations. Helpful charts and summaries are used to convey information such as exponential, square root,...

This more advanced Guide builds upon the reference material set out in the Introductory Algebra Guide. Linear equations, polynomial equations and complex numbers are readily explained; clear and easy to follow emphasis is ...

This Guide provides a concise and very readable summary of all key Algebraic principles. Special attention is directed to terminology, laws, and operations, with practical examples developed as illustration of these princi...

Vectors are an important area of study that develops naturally from a basic understanding of physics and is subsets – statics, dynamics, and mechanics. This practical Guide provides assistance in an often complex disciplin...